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采用变劲度系数的耦合弹簧构建一实际的两自由度弱非线性耦合系统, 用近似Lie对称性理论研究系统的一阶近似Lie对称性与近似守恒量, 得到6个一阶近似Lie对称性和一阶近似守恒量, 其中1个一阶近似守恒量实为系统的精确守恒量, 4个一阶近似守恒量为平凡的一阶近似守恒量, 只有1个一阶近似守恒量为稳定的一阶近似守恒量.
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关键词:
- 两自由度弱非线性耦合系统 /
- 近似Lie对称性 /
- 近似守恒量
A real weak nonlinear coupled two-dimensional system is constructed first by using coupling spring with variable force constant. The first-order approximate Lie symmetries and approximate conserved quantities of the system are studied. The system possesses six first-order approximate Lie symmetries and approximate conserved quantities, of which one is an exact conserved quantity, four are trivial conserved quantities, and only one is a stable conserved quantity.-
Keywords:
- weak nonlinear coupled two-dimensional system /
- approximate Lie symmetries /
- approximate conserved quantity
[1] Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems(Beijing: Science Press) p103, p303 (in Chinese) [梅凤翔 1999 李群和李代数对约束力学系统的应用(北京: 科学出版社)第103页, 第303页]
[2] Dong W S, Wang B X, Fang J H 2011 Chin. Phys. B 20 010204
[3] Chen R, Xu X J 2012 Chin. Phys. B 21 094510
[4] Fang J H 2010 Chin. Phys. B 19 040301
[5] Wang X X, Han Y L, Zhang M L, Jia L Q 2013 Chin. Phys. B 22 020201
[6] Xie Y L, Jia L Q, Luo S K 2011 Chin. Phys. B 20 010203
[7] Jiang W A, Luo S K 2011 Acta Phys. Sin. 60 060201 (in Chinese) [姜文安, 罗绍凯 2011 60 060201]
[8] Han Y L, Sun X T, Zhang Y Y, Jia L Q 2013 Acta Phys. Sin. 62 160201 (in Chinese)[韩月林, 孙现亭, 张耀宇, 贾利群 2013 62 160201]
[9] Leach P G L, Moyo S, Cotsakis S, Lemmer R L 2001 J. Nonlinear Math. Phys. 1 139
[10] Govinder K S, Heil T G, Uzer T 1998 Phys. Lett. A 240 127
[11] Kara A H, Mahomed F M, Unal G 1999 Int. J. Theoret. Phys. 38 2389
[12] Unal G 2000 Phys. Lett. A 269 13
[13] Unal G 2001 Nonlinear Dyn. 26 309
[14] Unal G, Gorali G 2002 Nonlinear Dyn. 28 195
[15] Feroze T, Kara A H 2002 Int. J. Non-linear Mech. 37 275
[16] Ibragimov N H, Unal G, Jogreus C 2004 J. Math. Anal. Appl. 297 152
[17] Dolapci I T, Pakdemirli M 2004 Int. J. Non-linear Mech. 39 1603
[18] Kara A H, Mahomed F M, Qadir A 2008 Nonlinear Dyn. 51 183
[19] Pakdemirli M, Yurusoy M, Dolapci I T 2004 Acta Appl. Math. 80 243
[20] Johnpillai A G, Kara A H, Mahomed F M 2006 Int. J. Non-linear Mech. 41 830
[21] Grebenev V N, Oberlack M 2007 J. Nonlinear Math. Phys. 14 157
[22] Johnpillai A G, Kara A H, Mahomed F M 2009 J. Comput. Appl. Math. 223 508
[23] Lou Z M 2010 Acta Phys. Sin. 59 6764 (in Chinese) [楼智美 2010 59 6764]
[24] Lou Z M, Mei F X, Chen Z D 2012 Acta Phys. Sin. 61 110204 (in Chinese) [楼智美, 梅凤翔, 陈子栋 2012 61 110204]
[25] Zhang Z Y, Yong X L, Chen Y F 2009 Chin. Phys. B 19 2629
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[1] Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems(Beijing: Science Press) p103, p303 (in Chinese) [梅凤翔 1999 李群和李代数对约束力学系统的应用(北京: 科学出版社)第103页, 第303页]
[2] Dong W S, Wang B X, Fang J H 2011 Chin. Phys. B 20 010204
[3] Chen R, Xu X J 2012 Chin. Phys. B 21 094510
[4] Fang J H 2010 Chin. Phys. B 19 040301
[5] Wang X X, Han Y L, Zhang M L, Jia L Q 2013 Chin. Phys. B 22 020201
[6] Xie Y L, Jia L Q, Luo S K 2011 Chin. Phys. B 20 010203
[7] Jiang W A, Luo S K 2011 Acta Phys. Sin. 60 060201 (in Chinese) [姜文安, 罗绍凯 2011 60 060201]
[8] Han Y L, Sun X T, Zhang Y Y, Jia L Q 2013 Acta Phys. Sin. 62 160201 (in Chinese)[韩月林, 孙现亭, 张耀宇, 贾利群 2013 62 160201]
[9] Leach P G L, Moyo S, Cotsakis S, Lemmer R L 2001 J. Nonlinear Math. Phys. 1 139
[10] Govinder K S, Heil T G, Uzer T 1998 Phys. Lett. A 240 127
[11] Kara A H, Mahomed F M, Unal G 1999 Int. J. Theoret. Phys. 38 2389
[12] Unal G 2000 Phys. Lett. A 269 13
[13] Unal G 2001 Nonlinear Dyn. 26 309
[14] Unal G, Gorali G 2002 Nonlinear Dyn. 28 195
[15] Feroze T, Kara A H 2002 Int. J. Non-linear Mech. 37 275
[16] Ibragimov N H, Unal G, Jogreus C 2004 J. Math. Anal. Appl. 297 152
[17] Dolapci I T, Pakdemirli M 2004 Int. J. Non-linear Mech. 39 1603
[18] Kara A H, Mahomed F M, Qadir A 2008 Nonlinear Dyn. 51 183
[19] Pakdemirli M, Yurusoy M, Dolapci I T 2004 Acta Appl. Math. 80 243
[20] Johnpillai A G, Kara A H, Mahomed F M 2006 Int. J. Non-linear Mech. 41 830
[21] Grebenev V N, Oberlack M 2007 J. Nonlinear Math. Phys. 14 157
[22] Johnpillai A G, Kara A H, Mahomed F M 2009 J. Comput. Appl. Math. 223 508
[23] Lou Z M 2010 Acta Phys. Sin. 59 6764 (in Chinese) [楼智美 2010 59 6764]
[24] Lou Z M, Mei F X, Chen Z D 2012 Acta Phys. Sin. 61 110204 (in Chinese) [楼智美, 梅凤翔, 陈子栋 2012 61 110204]
[25] Zhang Z Y, Yong X L, Chen Y F 2009 Chin. Phys. B 19 2629
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